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Mirrors > Home > ILE Home > Th. List > Mathboxes > sscoll2 | Unicode version |
Description: Version of ax-sscoll 13112 with two disjoint variable conditions removed and without initial universal quantifiers. (Contributed by BJ, 5-Oct-2019.) |
Ref | Expression |
---|---|
sscoll2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1493 | . . 3 | |
2 | nfv 1493 | . . . 4 | |
3 | simpl 108 | . . . . . 6 | |
4 | rexeq 2604 | . . . . . . 7 | |
5 | 4 | adantl 275 | . . . . . 6 |
6 | 3, 5 | raleqbidv 2615 | . . . . 5 |
7 | nfv 1493 | . . . . . 6 | |
8 | nfv 1493 | . . . . . . 7 | |
9 | rexeq 2604 | . . . . . . . . 9 | |
10 | 9 | adantr 274 | . . . . . . . 8 |
11 | 10 | bibi2d 231 | . . . . . . 7 |
12 | 8, 11 | albid 1579 | . . . . . 6 |
13 | 7, 12 | rexbid 2413 | . . . . 5 |
14 | 6, 13 | imbi12d 233 | . . . 4 |
15 | 2, 14 | albid 1579 | . . 3 |
16 | 1, 15 | exbid 1580 | . 2 |
17 | ax-sscoll 13112 | . . . 4 | |
18 | 17 | spi 1501 | . . 3 |
19 | 18 | spi 1501 | . 2 |
20 | 16, 19 | ch2varv 12902 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wex 1453 wral 2393 wrex 2394 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sscoll 13112 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 |
This theorem is referenced by: (None) |
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